Compatible stem volume and taper equations for Cilicica fir

Öz

Four taper estimating systems were evaluated for Cilicica fir (Abies cilicica Carr.) in Turkey to demonstrate statistical and practical considerations that should be used when selecting a taper estimating system for forest inventory purposes. The four equations selected were: Kozak et al. (1969), Demaerschalk (1972), Max and Burkhart (1976), and Clark et al. (1991). Tested models have been compared using evaluation statistics like as: mean difference (MD), standard error of the estimate (SEE), and Fit index (FI). Clark et al. (1991)’s segmented taper model was superior in predicting Cilicica fir stem form and stem volume than the other models. However, since this model also requires the measurement of the upper stem diameter value at 5.30 m for stem diameter and volume estimations, it was concluded that Max and Burkhart (1976) model is more suitable for practical forestry purposes among the models tested. Clark et al.’s, Max and Burkhart’s, and Demaerschalk’s models showed consistent prediction performances for both the whole stem and different parts of the stem in terms of MD and SEE values in diameter and volume estimates. Average diameter and volume prediction errors were less than 2.0 cm and 0.01 m3, respectively. All models produced reliable results for diameter and merchantable taper volume estimates at any point, based on 10 different relative height classes.

Anahtar Kelimeler

• Compatible stem diameter model
• Taper and volume
• Abies cilicica

Toros göknarı için uyumlu hacim ve gövde çapı modelleri

Öz

Bu çalışmada, orman envanteri uygulamaları için bir gövde çapı modelinin seçiminde kullanılabilecek istatistiksel ve pratik hususları göstermek amacıyla Toros göknarı (Abies cilicica Carr.) için dört gövde çapı modeli karşılaştırmalı olarak değerlendirilmiştir. Bu amaçla Kozak vd. (1969), Demaerschalk (1972), Max ve Burkhart (1976) ve Clark vd. (1991) tarafından geliştirilen uyumlu gövde çapı modelleri seçilmiştir. Modeller, ortalama hata (MD), tahminlerin standart hatası (SEE) ve uyum indeksi (FI) ölçüt değerleri kullanılarak karşılaştırılmıştır. Çalışma sonucunda, Clark vd. (1991) tarafından geliştirilen modelin gövde çapı ve gövde hacmi tahminlerinde diğer modellerden daha üstün olduğu görülmüştür. Ancak bu model gövde çapı ve hacim tahminleri için 5.30 m’deki çap değerine de ihtiyaç duyması nedeniyle Max ve Burkhart (1976) modelinin test edilen modeller arasında pratik ormancılık uygulamaları için daha uygun olduğu sonucuna varılmıştır. Clark vd. (1991), Max ve Burkhart (1976) ve Demaerschalk (1972) modelleri çap ve hacim tahminlerindeki MD ve SEE değerleri bakımından hem tüm gövde hem de gövdenin farklı bölümleri için tutarlı tahmin performansları göstermiştir. Test edilen modeller için çap tahminlerindeki ortalama hata 2.0 cm’den, hacim tahminlerindeki ortalama hata ise 0.01 m3’ten daha azdır. Karşılaştırılan tüm modeller, 10 farklı nispi boy sınıfı esas alındığında, herhangi bir noktadaki çap ve ticari gövde hacim tahminleri için güvenilir sonuçlar üretmiştir.

Anahtar Kelimeler

• Uyumlu gövde çapı modeli
• Gövde çapı ve hacim
• Toros göknarı

Kaynakça

1. Alkan, O., Ozçelik, R., Alkan, H. 2019. Development of regional stem taper models for some important tree species of Turkey: Case study of Bucak. Turkish Journal of Forestry, 20(4): 333-340.
2. Bailey, R.L., 1995. Upper stem volumes from stem analysis data: An overlapping bolts method. Canadian Journal of Forest Research, 25(1):170-173.
3. Bi, H., 2000. Trigonometric variable-form taper equations for Australian eucalypts. Forest Science, 46(3):397-409.
4. Biging, G.S., 1984. Taper equations for second-growth mixed conifers of Northern California. Forest Science, 30(4): 1103-1117.
5. Brooks, J.R., Jiang, L., Ozçelik, R., 2008. Compatible stem volume and taper equations for Brutian pine, Cedar of Lebanon, and Cilicica fir in Turkey. Forest Ecology and Management, 256(1-2): 147-151.
6. Cao, Q.V., Burkhart, H.E., Max, T.A., 1980. Evaluation of two methods for cubic-volume prediction of loblolly pine to any merchantable limit. Forest Science, 26(1), 71-80.
7. Clark, III, A., Souter, R.A., Schlaegel, B.E., 1991. Stem profile equations for southern tree species. USDA For. Serv. Res. Pap. SE-282.
8. Coble, D.W., Hilpp, K., 2006. Compatible cubic-foot stem volume and upper-stem diameter equations for semi-intensive plantation grown loblolly pine trees in East Texas. Southern Journal of Applied Forestry, 30(3): 132-141.

9. Demaerschalk, J.P., 1972. Converting volume equations to compatible taper equations. Forest Science, 18(3):241-245.
10. Demaerschalk, J.P., Kozak, A., 1977. The whole-bole system: A conditioned dual-equation system for precise prediction of tree profiles. Canadian Journal of Forest Research, 7(3):488-497.
11. Eker, M., Poudel, K.P., Özçelik, R., 2017. Aboveground biomass equations for small trees of brutian pine in Turkey to facilitate harvesting and management. Forests, 8(12): 477.
12. Fang, Z., Borders, B.E., Bailey, R.L., 2000. Compatible volume-taper models for loblolly and slash pine based on a system with segmented-stem form factors. Forest Science, 46(1):1-12.
13. Figueiredo-Filho, A., Borders, B.E., Hitch, K.L., 1996. Taper equations for Pinus taeda plantations in Southern Brazil. Forest Ecology and Management, 83(1-2):39-46.
14. Hilt, D.E., 1980. Taper-based system for estimating stem volume of upland oaks. USDA For. Serv. Res. Pap. NE-458,12 p.
15. Hussain, A., Shahzad, M.K., He, P., Jiang, L., 2020. Stem taper equations for three major conifer species of Northeast China. Scandinavian Journal of Forest Research, 35(8): 562-576.
16. Hussain, A., Shahzad, M.K., Burkhart, H.E., Jiang, L., 2021. Stem taper functions for white birch (Betula platyphylla) and costata birch (Betula costata) in the Xiaoxing’an Mountains, northeast China. Forestry: An International Journal of Forest Research.
17. Jiang, L., Brooks, J.R., Wang, J., 2005. Compatible taper and volume equations for yellow-poplar in West Virginia. Forest ecology and management, 213(1-3): 399-409.
18. Jiang, L., Brooks, J.R., Hobbs, G.R., 2007. Using crown ratio in yellow-poplar compatible taper and volume equations. Northern Journal of Applied Forestry, 24(4): 271-275.
19. Jordan, L., Berenhaut, K., Souter, R., Daniels, R.F., 2005. Parsimonious and completely compatible taper, total, and merchantable volume models. Forest science, 51(6):578-584.
20. Kozak, A., 2004. My last words on taper equations. The Forestry Chronicle, 80(4):507-515.
21. Kozak, A., 1988. A variable-exponent taper equation. Canadian Journal of Forest Research, 18(11): 1363-1368.
22. Kozak, A. 1997. Effects of multicollinearity and autocorrelation on the variable-exponent taper functions. Canadian Journal of Forest Research, 27(5): 619-629.
23. Kozak, A., Munro, D.D., Smith, J.H.G., 1969. Taper functions and their application in forest inventory. The Forestry Chronicle, 45(4): 278-283.
24. Kozak, A., Smith, J.H.G., 1993. Standards for evaluating taper estimating systems. The Forestry Chronicle, 69(4):438-444.
25. Martin, A.J., 1981. Taper and volume equations for selected Appalachian hardwood species. USDA For. Serv. Res. Pap. NE-490.
26. Max, T.A., Burkhart, H.E., 1976. Segmented polynomial regression applied to taper equations. Forest Science, 22(3): 283-289.
27. McTague, J.P., Bailey, R.L., 1987. Simultaneous total and merchantable volume equations and a compatible taper function for loblolly pine. Canadian Journal of Forest Research, 17(1): 87-92.
28. McTague, J.P., Weiskittel, A., 2021. Evolution, history, and use of stem taper equations: a review of their development, application, and implementation. Canadian Journal of Forest Research, 51(2):210-235.
29. Newnham, R.M., 1988. A variable form taper function. Information Report PI-X-83. Forestry, Canada, p. 33.
30. Newnham, R.M., 1992. Variable-form taper functions for four Alberta tree species. Canadian Journal of Forest Research, 22(2): 210-223.
31. OGM, 2006. Orman Kaynakları. Orman Genel Müdürlüğü, Ankara, 159s.
32. Ormerod, D.W., 1986. The diameter-point method for tree taper description. Canadian Journal of Forest Research, 16(3): 484-490.
33. Ormerod, D.W., 1973. A simple bole model. The Forestry Chronicle, 49(3): 136-138.
34. Özçelik, R., Crecente-Campo, F., 2016. Stem taper equations for estimating merchantable volume of Lebanon cedar trees in the Taurus Mountains, Southern Turkey. Forest Science, 62(1):78.
35. Özçelik, R., Alkan, H., 2012. Okaliptüs ağaçlandırmaları için uyumlu gövde çapı ve gövde hacim modellerinin geliştirilmesi. Kahramanmaraş Sütçüimam Üniversitesi Doğa Bilimleri Dergisi, 15:247-254.
36. SAS Institute Inc., 2002. SAS/ETS User’s Guide, Version 9.0, SAS Institute Inc., Cary, NC.
37. Schlaegel, B.E., 1981. Testing, reporting, and using biomass estimation models. Southern Forest Biomass Workshop, 11-12 June, Georgetown, South Carolina, USA, pp. 95-112.
38. Shahzad, M.K., Hussain, A., Jiang, L., 2020. A model form for stem taper and volume estimates of Asian white birch (Betula platyphylla): a major commercial tree species of Northeast China. Canadian Journal of Forest Research, 50(3): 274-286.
39. Shahzad, M.K., Hussain, A., Burkhart, H.E., Li, F., Jiang, L., 2021. Stem taper functions for Betula platyphylla in the Daxing’an Mountains, northeast China. Journal of Forestry Research, 32: 529-541.
40. Sharma, M., Oderwald, R.G., 2001. Dimensionally compatible volume and taper equations. Canadian Journal of Forest Research, 31(5): 797-803.
41. Sharma, M., Parton, J., 2009. Modeling stand density effects on taper for jack pine and black spruce plantations using dimensional analysis. Forest science, 55(3): 268-282.
42. Thomas, C.E., Parresol, B.R., 1991. Simple, flexible, trigonometric taper equations. Canadian Journal of Forest Research, 21(7): 1132-1137.
43. Williams, M.S., Reich, R.M., 1997. Exploring the error structure of taper equations. Forest science, 43(3): 378-386.
44. Zakrzewski, W.T., MacFarlane, D.W., 2006. Regional stem profile model for cross-border comparisons of harvested red pine (Pinus resinosa Ait.) in Ontario and Michigan. Forest Science, 52(4): 468-475.